Ratio, Proportion and Percentages Formulas and Tricks

Ratio & Proportion

  • The equality of two ratios is called a proportion. If Equation , we write Equation and we say that a, b, c, d are in proportion. In a proportion, the first and fourth terms are known as extremes, while the second and third are known as means.

  • Equation

  • Mean proportion between a and b is

  • The compounded ratio of the ratios Equation is Equation

  • Equation is a duplicate ratio of Equation

  • Equation is a sub-duplicate ration of Equation

  • Equation is a triplicate ratio of Equation

  • Equation is a sub-triplicate ratio of Equation

  • If Equation , then Equation , which is called the Componendo.

  • If Equation , which is called the dividendo

  • If Equation , which is called the componendo & dividendo.

  • Variation: We say that x is directly proportional to y if Equation for some constant k and we write, Equation

  • Also, we say that x is inversely proportional to y Equation for some constant k and we write Equation

Ratios

  • Equation

  • If Equation then for a positive quantity x,

  • Equation If Equation then for a positive quantity x,

  • Equation

Proportions

Equation

  • Equation

  • Equation

  • Equation

  • Equation

  • Equation

  • Equation

  • Equation

Percentage

  • To express x% as a fraction, we have Equation

  • To express Equation as a percent, we have Equation

  • If ‘A’ is R% more than ‘B’, then ‘B’ is less than ‘A’ by

    OR

    If the price of a commodity increases by R%, then the reduction in consumption, not to increase the expenditure is Equation

  • If ‘A’ is R% less than ‘B’, then ‘B’ is more than ‘A’ by

    OR

    If the price of a commodity decreases by R%, then the increase in consumption, not to increase the expenditure is Equation

  • If the population of a town is ‘P’ in a year, then its population after ‘N’ years is Equation

  • If the population of a town is ‘P’ in a year, then its population ‘N’ years ago is Equation

Percentage Change

  • Equation

  • For two successive changes of Equation and Equation Equation